Linking electromagnetic and gravitational radiation in coalescing binary neutron stars

We expand on our study of the gravitational and electromagnetic emissions from the late stage of an inspiraling neutron star binary as presented in Palenzuela et al. [Phys. Rev. Lett. 111, 061105 (2013)]. Interactions between the stellar magnetospheres, driven by the extreme dynamics of the merger, can yield considerable outflows. We study the gravitational and electromagnetic waves produced during the inspiral and merger of a binary neutron star system using a full relativistic, resistive magnetohydrodynamics evolution code. We show that the interaction between the stellar magnetospheres extracts kinetic energy from the system and powers radiative Poynting flux and heat dissipation. These features depend strongly on the configuration of the initial stellar magnetic moments. Our results indicate that this power can strongly outshine pulsars in binaries and have a distinctive angular and time-dependent pattern. Our discussion provides more detail than Palenzuela et al., showing clear evidence of the different effects taking place during the inspiral. Our simulations include a few milliseconds after the actual merger and study the dynamics of the magnetic fields during the formation of the hypermassive neutron star. We also briefly discuss the possibility of observing such emissions.

Figure 1

Trajectory of the binary as measured by the location of the maximum densities as functions of time. The system undergoes about 2.5 orbits before the stars come into contact.

Figure 2

The dominant $l=m=2$ mode of the gravitational wave extracted at $R_{\mathrm{ext}}=180\mathrm{km}$. The time $t=0$ is set as the moment when the stars first make contact.

Figure 3

$U/D$ case. Top-down view of certain magnetic field lines along with the stellar density at $t=-1.7\mathrm{ms}$. Only field lines originating along a line connecting the stars slightly above the equatorial plane are shown for clarity. Similar plots for the other cases are shown in Fig. 6 ($U/U$) and Fig. 9 ($U/u$). Note that reconnections near the leading edges of the stars (orbiting counterclockwise in this view) have severed some lines which would otherwise connect the stars.

Figure 4

$U/D$ case. Snapshots of the magnetic field configuration on the $y=0$ plane at half-orbital periods (times $t=-4.6$, $-3.2$, $-1.7$ and $-0.5\mathrm{ms}$). Poloidal field lines are shown while the component perpendicular to the plane (related to the toroidal component) is shaded in color. Similar plots for the other cases are shown in Fig. 7 ($U/U$) and Fig. 10 ($U/u$). The field lines connecting the stars result from reconnection. Note that after each half-orbit, the direction of the perpendicular component switches direction due to the change in sign of the poloidal field.

Figure 5

$U/D$ case. Representative snapshot of the magnetic field configuration and induced current sheet at $t=-2.9\mathrm{ms}$.

Figure 6

$U/U$ case. Top-down view of certain magnetic field lines along with the stellar density at $t=-1.7\mathrm{ms}$. Similar plots for the other cases are shown in Fig. 3 ($U/D$) and Fig. 9 ($U/u$). The repulsion of roughly aligned field lines is clearly visible at the midplane between the stars.

Figure 7

$U/U$ case. Snapshots of the magnetic field configuration on the $y=0$ plane at half-orbital periods (times $t=-4.6$, $-3.2$, $-1.7$ and $-0.5\mathrm{ms}$). Similar plots for the other cases are shown in Fig. 4 ($U/D$) and Fig. 10 ($U/u$). Note that field lines near the midplane repel each other as is more evident in Fig. 6. Far from the binary at large radii, the magnetic field structure resembles that of an aligned rotator. Indeed the direction of the magnetic field changes across the equatorial plane and a Y point arises as the orbit tightens.

Figure 8

$U/U$ case. Snapshot of the magnetic field configuration and induced current sheet at $t=-2.9\mathrm{ms}$.

Figure 9

$U/u$ case. Top-down view of certain magnetic field lines along with the stellar density at $t=-1.7\mathrm{ms}$. Similar plots for the other cases are shown in Fig. 3 ($U/D$) and Fig. 6 ($U/U$). Note that field lines emanating from the strongly magnetized star bend both around the weaker star and the region just in front of it (the stars are orbiting counterclockwise). Similarly, the lines behind the weaker star are distorted by a trailing current sheet.

Figure 10

$U/u$ case. Snapshots of the magnetic field configuration on the $y=0$ plane at half-orbital periods (times $t=-4.6$, $-2.9$, $-1.7$ and $-0.5\mathrm{ms}$). Similar plots for the other cases are shown in Fig. 4 ($U/D$) and Fig. 7 ($U/U$). Notice that the magnetic field structure is mainly described by an orbiting dipole perturbed by the interaction with the weakly magnetized companion and its trailing current sheet.

Figure 11

$U/u$ case. Snapshot of the magnetic field configuration and current sheet at $t=-1.7\mathrm{ms}$.

Figure 12

Currents (drawn as arrows) and charge density (color coded) for the $U/D$ (first panel), $U/U$ (second panel) and $U/u$ (third panel) case at $t=-4.6\mathrm{ms}$. In all cases an effective circuit arises; however the circuits extend significantly in both vertical directions for the first two cases which contrasts with the more localized circuit in the last case. The bottom panel resembles the diagram in Fig. 1 of 7.

Figure 13

Poynting flux as a volume rendering (left) and evaluated on an encompassing sphere (right) at $t=-2.9\mathrm{ms}$. The $U/D$ case (top row), the $U/U$ case (middle row) and the $U/u$ (bottom row) cases are shown. The sphere is located at a radius $r=80\mathrm{km}$. The top two cases radiate more strongly away from the equatorial plane than that of the $U/u$ case. The $U/u$ case radiates quite asymmetrically in the direction of the more magnetized star and mostly near the orbital plane.

Figure 14

Electromagnetic luminosity for the three different magnetic field configurations. Additionally, three curves illustrating $L\propto {\Omega }^p$ with $p=\{3/2,14/3,12\}$ are shown as guidance. The maximum of the gravitational radiation, marked with a vertical dashed line, occurs approximately at $t\approx 1.48\mathrm{ms}$.

Figure 15

Polarity (red positive, blue negative) of the $B_z$ component of the magnetic field at $z=+7.4\mathrm{km}$ above the orbital plane at late times ($t\approx 1.4\mathrm{ms}$; after the stars have already touched) for the $U/D$, $U/U$ and $U/u$ cases respectively. The pattern resembles a “striped” pattern. The density of the merging binary is also shown at the center of the figures.